Stochastic six-vertex model

DOI10.1215/00127094-3166843zbMath1343.82013arXiv1407.6729OpenAlexW1449099541MaRDI QIDQ267530

Ivan Corwin, Vadim Gorin, Alexei Borodin

Publication date: 8 April 2016

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.6729

zbMATH Keywords

Markov chainsobservablesinteracting particle systemsmarginalsasymmetric simple exclusion process (ASEP)asymptotic limit shapeBoltzmann weightsGUE Tracy-Widom distributionKPZ universalityrandom height functionrandom-matrix theorysix-vertex (square ice) model: stochastic six-vertex modelspectral decomposition of the transfer matrixstochastic transfer matrixTASEP (totally ASEP)

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Groups and algebras in quantum theory and relations with integrable systems (81R12) Stochastic matrices (15B51) Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics (82C24) Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems (37P30)

Related Items (81)

The ASEP and determinantal point processes ⋮ Stochastic six-vertex model in a half-quadrant and half-line open asymmetric simple exclusion process ⋮ Integrable structure of multispecies zero range process ⋮ Constrained percolation in two dimensions ⋮ Hall-Littlewood RSK field ⋮ Stochastic higher spin vertex models on the line ⋮ Inhomogeneous exponential jump model ⋮ Absorbing time asymptotics in the oriented swap process ⋮ Exceedingly large deviations of the totally asymmetric exclusion process ⋮ Stochastic symplectic ice ⋮ Dynamical stochastic higher spin vertex models ⋮ Arctic curves of the six-vertex model on generic domains: the tangent method ⋮ Limit distributions for KPZ growth models with spatially homogeneous random initial conditions ⋮ Convergence of the stochastic six-vertex model to the ASEP, stochastic six-vertex model and ASEP ⋮ Symmetric elliptic functions, IRF models, and dynamic exclusion processes ⋮ Lower tail of the KPZ equation ⋮ Observables of coloured stochastic vertex models and their polymer limits ⋮ Density and current profiles in \(\operatorname{U}_q(A_2^{(1)})\) zero range process ⋮ Stochastic PDE limit of the six vertex model ⋮ Limit shapes and local statistics for the stochastic six-vertex model ⋮ Lozenge tilings with free boundaries ⋮ Arctic curves of the 20V model on a triangle ⋮ Arctic curves of the four-vertex model ⋮ A stochastic telegraph equation from the six-vertex model ⋮ An Ising-type formulation of the six-vertex model ⋮ Enumerative combinatorics. Abstracts from the workshop held December 11--17, 2022 ⋮ On the transition between the disordered and antiferroelectric phases of the 6-vertex model ⋮ KPZ limit theorems ⋮ Stationary measure for six-vertex model on a strip ⋮ Shift-invariance of the colored TASEP and finishing times of the oriented swap process ⋮ Shift‐invariance for vertex models and polymers ⋮ Nonexistence and uniqueness for pure states of ferroelectric six‐vertex models ⋮ The stochastic heat equation with multiplicative Lévy noise: existence, moments, and intermittency ⋮ Classification of stationary distributions for the stochastic vertex models ⋮ Boundary current fluctuations for the half‐space ASEP and six‐vertex model ⋮ Cutoff profile of the metropolis biased card shuffling ⋮ Construction ofR-matrices for symmetric tensor representations related to ${U}_{q}(\hat{{{sl}}_{n}})$ ⋮ HALF-SPACE MACDONALD PROCESSES ⋮ GOE fluctuations for the maximum of the top path in alternating sign matrices ⋮ Strong law of large numbers for the stochastic six vertex model ⋮ Irreversible Markov dynamics and hydrodynamics for KPZ states in the stochastic six vertex model ⋮ Current fluctuations of the stationary ASEP and six-vertex model ⋮ PushTASEP in inhomogeneous space ⋮ Two-point convergence of the stochastic six-vertex model to the Airy process ⋮ Probabilistic cellular automata with memory two: invariant laws and multidirectional reversibility ⋮ Deducing a variational principle with minimal \textit{a priori} assumptions ⋮ Stochastic higher spin six vertex model and Macdonald measures ⋮ Stochastic telegraph equation limit for the stochastic six vertex model ⋮ Arctic curve of the free-fermion six-vertex model in an L-shaped domain ⋮ Stochastic Duality and Orthogonal Polynomials ⋮ Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz ⋮ Higher spin six vertex model and symmetric rational functions ⋮ Transversal fluctuations of the ASEP, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles ⋮ An algebraic construction of duality functions for the stochastic \(\mathcal U_q(A_n^{(1)})\) vertex model and its degenerations ⋮ Random-walk in beta-distributed random environment ⋮ Stochastic higher spin six vertex model and \(q\)-TASEPs ⋮ Parameter permutation symmetry in particle systems and random polymers ⋮ Large deviations for sticky Brownian motions ⋮ Markov duality for stochastic six vertex model ⋮ Random tilings with the GPU ⋮ KPZ equation limit of stochastic higher spin six vertex model ⋮ On a family of symmetric rational functions ⋮ Limit shapes of the stochastic six vertex model ⋮ Self-duality of Markov processes and intertwining functions ⋮ Color-position symmetry in interacting particle systems ⋮ Yang-Baxter random fields and stochastic vertex models ⋮ The stochastic telegraph equation limit of the stochastic higher spin six vertex model ⋮ Free field approach to the Macdonald process ⋮ Boundary matrices for the higher spin six vertex model ⋮ Refined Cauchy identity for spin Hall-Littlewood symmetric rational functions ⋮ Observables of stochastic colored vertex models and local relation ⋮ Upper-tail large deviation principle for the ASEP ⋮ GUE corners process in boundary-weighed six-vertex models ⋮ YANG–BAXTER FIELD FOR SPIN HALL–LITTLEWOOD SYMMETRIC FUNCTIONS ⋮ A variational principle for a non-integrable model ⋮ Stationary stochastic higher spin six vertex model and \(q\)-Whittaker measure ⋮ Orthogonal dualities of Markov processes and unitary symmetries ⋮ Hidden diagonal integrability of q-Hahn vertex model and beta polymer model ⋮ Non-probabilistic fermionic limit shapes ⋮ Spin \(q\)-Whittaker polynomials and deformed quantum Toda ⋮ Integrable boundaries for the q-Hahn process

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Log-gamma polymer free energy fluctuations via a Fredholm determinant identity
• Anisotropic growth of random surfaces in \({2+1}\) dimensions
• Formulas and asymptotics for the asymmetric simple exclusion process
• From alternating sign matrices to the Gaussian unitary ensemble
• From duality to determinants for \(q\)-TASEP and ASEP
• Asymptotics of uniformly random lozenge tilings of polygons. Gaussian free field
• Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz
• On the weighted enumeration of alternating sign matrices and descending plane partitions
• The \(q\)-Gelfand-Tsetlin graph, Gibbs measures and \(q\)-Toeplitz matrices
• Alternating-sign matrices and domino tilings. II
• Calculation of norms of Bethe wave functions
• Tracy-Widom asymptotics for \(q\)-TASEP
• Integral formulas for the asymmetric simple exclusion process
• Large time asymptotics of growth models on space-like paths. I: Push ASEP
• Asymptotics in ASEP with step initial condition
• The asymmetric six-vertex model
• Interaction of Markov processes
• Level-spacing distributions and the Airy kernel
• Stochastic Burgers and KPZ equations from particle systems
• Scale invariance of the PNG droplet and the Airy process
• Discrete polynuclear growth and determinantal processes
• Shape fluctuations and random matrices
• Integrable probability: from representation theory to MacDonald processes
• Macdonald processes
• Eigenvalues of GUE minors
• Limit shapes and the complex Burgers equation
• The arctic circle boundary and the Airy process
• Dimers and amoebae
• Height fluctuations in the honeycomb dimer model
• Continuum limit for some growth models.
• A variational principle for domino tilings
• Percolation and number of phases in the two-dimensional Ising model
• Random Matrices and the Six-Vertex Model
• CLT for spectra of submatrices of Wigner random matrices
• THE KARDAR–PARISI–ZHANG EQUATION AND UNIVERSALITY CLASS
• General β-Jacobi Corners Process and the Gaussian Free Field
• Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions
• Dynamic Scaling of Growing Interfaces
• Two Ways to Solve ASEP
• Fully Packed Loop Models on Finite Geometries
• Non-equilibrium behaviour of a many particle process: Density profile and local equilibria
• AsymmetricXXZchain at the antiferromagnetic transition: spectra and partition functions
• Phase diagram of the non-Hermitian asymmetricXXZspin chain
• Six-vertex model, roughened surfaces, and an asymmetric spin Hamiltonian
• Lectures on integrable probability
• Lectures on the integrability of the 6-vertex model
• Macdonald processes, quantum integrable systems and the Kardar-Parisi-Zhang universality class
• Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension
• Domino tilings and the six-vertex model at its free-fermion point
• Asymptotics of symmetric polynomials with applications to statistical mechanics and representation theory

This page was built for publication: Stochastic six-vertex model